Further results on essential Nash equilibria in normal-form games

Abstract

A Nash equilibrium x of a normal-form game G is essential if any perturbation of G has an equilibrium close to x. Using payoff perturbations, we identify a new collection of games containing a dense, residual subset of games whose Nash equilibria are all essential. This collection covers economic examples that cannot be handled by extant results and subsumes the sets of games considered in the literature.

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

“…Yu and Xiang [26] proposed an essential set for Nash equilibria and proved the existence of essential component in the second direction by considering perturbations of payoff functions of players. There is a lot of researches about using the essential component to discuss the stability of Nash equilibria (see, [1,2,8,17,18,24,25,27]). However, there are two drawbacks in the second way.…”

Generic Stability of the Weakly Pareto-Nash Equilibrium with Strategy Transformational Barriers

“…Afterwards, Yu and Luo and Yu [10,11] extended previous work to the general n-person noncooperative game, generalized game, or other games by using entirely different approaches. Recently, Scalzo [12,13] and Carbonell-Nicolau and Carbonell-Nicolau and Wohl [14,15] provided some extensions about discontinuous payoffs and further studied the essential stability of discontinuous games. Yang and Zhang [16] proved some existence and essential stability results of cooperative equilibrium for population games.…”